Problem: Simplify the following expression: ${3(-t+1)-(2-2t)}$
Distribute the ${3}$ into the first set of parentheses: $ {3(}\gray{-t+1}{)} - (2-2t) $ $ {-3t+3} - (2-2t) $ The minus sign in front of the parentheses means we multiply each term inside the parentheses by ${-1}$ $ -3t+3 {-1(}\gray{2-2t}{)} $ $ -3t+3 {-2+2t} $ Rewrite the expression to group the ${t}$ terms and numeric terms: $ {-3t + 2t} + {3 - 2}$ Combine the ${t}$ terms: $ {-t} + {3 - 2}$ Combine the numeric terms: $ {-t} + {1}$ The simplified expression is $-t+1$